The Fundamental Principle of Counting (Leaving Cert Mathematics): Flashcards

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The Fundamental Principle of Counting
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Fundamental Principle of Counting

Calculates total ways for sequential tasks

Task 1: xx ways, Task 2: yy ways. Total?

x×yx \times y ways

General formula: nn sequential tasks

Ways for task1 ×\times task2 ×\times ... ×\times taskn

Box method definition

Visual tool: one box per choice, multiply all

4 models, 3 colours. Total?

4×3=124 \times 3 = 12

11 players, captain & vice-captain. Ways?

11×10=11011 \times 10 = 110

1 letter + 2 diff digits (1-9). Codes?

26×9×8=1,87226 \times 9 \times 8 = 1,872

Counting paths between locations

Multiply routes between consecutive points

'And' in counting means...

Multiply

Sequential choices rule

Multiply the possibilities

Common exam applications

Teams, codes, meals, routes, arrangements, probability

Why fewer options in second choice?

Can't repeat if without replacement

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